If the image of quadratic function f (x) passes through point (0,0), and f (x +!) = f (x) + X + 1, find the analytic expression of F (x)

If the image of quadratic function f (x) passes through point (0,0), and f (x +!) = f (x) + X + 1, find the analytic expression of F (x)

If the image of quadratic function f [x] is known to pass through a [- 1,0] B [3,0], C [1, - 8]
Finding the analytic expression of F [x]
Find the maximum value of F [x] on & nbsp; X belonging to [0,3]
Finding the solution set of inequality f [x] greater than or equal to 0

Let f (x) = a (x + 1) (x-3), bring in (1, - 8): - 8 = a (1 + 1) (1-3) - 8 = - 4AA = 2, so f (x) = 2 (x + 1) (x-3), that is, f (x) = 2x ^ 2 - 4x-6. Because f (x) = 2x ^ 2 - 4x-6, the axis of symmetry is a straight line x = 1, when x ∈ [0,3], the function has the minimum value f (1) = - 8 and the maximum value f (3) = 18-12-6 = 0, that is, the maximum value

Given the image of quadratic function f (x), the analytic expression of F (x) can be obtained through three points a (- 1,3) B (0,1) C (2,3)
upper

Since W is a quadratic function, let y = ax ^ 2 + BX + C. If you take XY in, you will get ABC, then FX will come out

Given that f (x) is a quadratic function and the image passes through a (2. - 3), B (- 2. - 7) and C (0. - 3), what is the analytic expression of F (x)
Ask for detailed replacement process and description··

Replace the three-point coordinates into the standard form of quadratic function y = ax ^ 2 + BX + C, get the equations formed by three equations, solve a, B, C, you will know what the analytical formula is!